The pitcher begins by throwing the disc to the opposing team's current hitter, who then must catch the disc (under certain conditions, including distance away, height of the disc, etc.), and, if successful, throws it back into the field, which counts as a hit. If an attempt is made to catch the disc by the hitter, but fails for some reason, then that is a strike. Similarly, if the disc fails to fly into the established zone of height or vertical distance from the hitter, then it is considered a "disc" (a ball in baseball).
The rest of the game is played in a similar manner to baseball. If a fielder catches the disc thrown by the hitter, then they're out. Bases are run just like the ball game too.
The only real difference is if there is no catcher: if the fielding team manages to throw the disc over home plate before the runner on 3rd makes it home, then it counts as an out.